id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
41,077 |
255*257 + 1 = 256^2
|
11,126 |
(1 + \frac14)\cdot \left(1 - 1/4\right) = 1 - \dfrac{1}{16}
|
-6,131 |
\dfrac{3}{10 \cdot \left(-1\right) + 2 \cdot m} = \tfrac{3}{2 \cdot (m + 5 \cdot (-1))}
|
6,089 |
n + 3 \geq (n + (-1))\cdot 2 \Rightarrow 5 \geq n
|
-20,131 |
\frac{y\cdot (-81)}{90\cdot y} = -\frac{1}{10}\cdot 9\cdot 9\cdot y/(y\cdot 9)
|
10,949 |
2 l + (-1) = -(-l + 51) + 50 + l
|
11,171 |
\sin(x)\cdot \sin(y) = \sin\left(y\right)\cdot \sin(x)
|
19,048 |
6 \cdot (-1) + \sqrt{16} + 2 = 0
|
773 |
16 \cdot (|B \cdot D| - |C \cdot E|) = 64 \Rightarrow 4 \cdot (-1) + |B \cdot D| = |C \cdot E|
|
4,588 |
y^5 + \left(-1\right) = (y + (-1))*(y^4 + y^3 + y^2 + y + 1)
|
-23,229 |
\frac{\dfrac{5}{9}}{2}1 = 5/18
|
3,075 |
-2*x + 1 \lt -x + (-1) \implies x \gt 2
|
9,329 |
\int \frac{1}{y}\,\mathrm{d}y = (\ln(y))! = \ln(y)
|
-14,387 |
(7 + 8 \times 3) - 6 \times 8 = (7 + 24) - 6 \times 8 = 31 - 6 \times 8 = 31 - 48 = -17
|
-20,102 |
\frac{1}{4} \cdot 4 \cdot \frac{1}{(-1) \cdot 3 \cdot k} \cdot \left(-k + 9 \cdot (-1)\right) = \frac{1}{(-12) \cdot k} \cdot (36 \cdot (-1) - 4 \cdot k)
|
15,598 |
\sin\left(y\right) = \sin\left(y/2\right) \cos(\frac{y}{2})*2
|
-20,079 |
-\tfrac{1}{4}\times ((-1)\times 4\times t)/(t\times (-4)) = \dfrac{4\times t}{t\times (-16)}\times 1
|
30,177 |
-n + \frac{n}{-r + 1}*2 = n*\frac{1 + r}{-r + 1}
|
-11,936 |
\frac{8.712}{100} = 8.712\cdot 0.01
|
3,743 |
\frac{1}{4} 3 = 1^{-1}*3/4
|
-15,511 |
\frac{p^3}{\dfrac{1}{q^{20}}\cdot p^{12}} = \dfrac{1}{\frac{1}{q^{20}\cdot \frac{1}{p^{12}}}}\cdot p^3
|
19,257 |
\frac{\text{d}}{\text{d}y} (t \cdot t^{\dfrac{1}{2}}) = \frac{1}{2 \cdot t^{\frac{1}{2}}} \cdot t + t^{\frac{1}{2}} = \frac{1}{2} \cdot 3 \cdot t^{\frac{1}{2}}
|
-2,611 |
\sqrt{3}-\sqrt{27}+\sqrt{75} = \sqrt{3}-\sqrt{9 \cdot 3}+\sqrt{25 \cdot 3}
|
13,501 |
\pi*85/3 = \frac{1}{6}5 \pi*34
|
10,792 |
60 = 3!*\binom{5}{3}
|
33,150 |
\cos{\psi} \cdot \sin{Y} + \sin{\psi} \cdot \cos{Y} = \sin(Y + \psi)
|
7,830 |
-81 i = 81 \left(-i\right) = 81 (\cos(\tfrac{3\pi}{2}) + i\sin(\dfrac{3\pi}{2}1))
|
17,971 |
\left[b_1,b_2\right] = [b_1,b_2]
|
-20,244 |
\frac{1}{x + 4 \times \left(-1\right)} \times (x + 4 \times (-1)) \times (-\frac{10}{1}) = \frac{-x \times 10 + 40}{x + 4 \times (-1)}
|
1,916 |
x^6 + (-1) = (x^3 + 1) (x^3 + (-1))
|
48,009 |
(5 \cdot 5)^{1/2} = 5 = |5|
|
31,103 |
a^{1 + l} = a^{l + 1}
|
8,496 |
4 < y^2\Longrightarrow (y + 2 \cdot \left(-1\right)) \cdot (2 + y) \gt 0
|
27,765 |
8\cdot x = 90 \Rightarrow x = \frac{45}{4} = 11.25
|
10,468 |
det\left(Z\right) = det\left(Z_{k + \left(-1\right)}\right) = 1 \implies Z_{k + \left(-1\right)}
|
36,368 |
49*8 = 392
|
11,783 |
(x + b)^2 - x^2 - x*b + b^2 = x*b*3
|
-1,326 |
((-8)\cdot \frac{1}{3})/(1/7\cdot (-4)) = -7/4\cdot \left(-\frac83\right)
|
28,913 |
h + g \geq 2 \implies g \geq -h + 2
|
6,165 |
-C + E(T) = E(T - C)
|
-7,563 |
\frac{9 - i \cdot 9}{3 + i \cdot 3} = \frac{1}{-3 \cdot i + 3} \cdot (3 - 3 \cdot i) \cdot \dfrac{-i \cdot 9 + 9}{3 + i \cdot 3}
|
21,363 |
2 \cdot x + \left(-1\right) + 3 \cdot (-1) + 1 = 3 \cdot (-1) + 2 \cdot x
|
-3,122 |
125^{1/2} + 20^{1/2} = \left(25 \cdot 5\right)^{1/2} + (4 \cdot 5)^{1/2}
|
17,782 |
7578/24541 + 2 = \frac{1}{24541}*56660
|
2,595 |
k + 2*(-1) = k + 3*(-1) + 1
|
36,025 |
z^6 = z^3 z z^2 = z^2 z z z^2
|
-24,544 |
\dfrac{1}{3 + 5}\cdot 32 = 32/8 = 32/8 = 4
|
8,749 |
h/g*\frac1x*c = c/x*\frac1g*h
|
-2,807 |
2^{\dfrac{1}{2}}*25^{\dfrac{1}{2}} - 16^{\frac{1}{2}}*2^{1 / 2} = 2^{\frac{1}{2}}*5 - 4*2^{1 / 2}
|
-2,664 |
(3 + 4 + 5)\cdot \sqrt{3} = 12\cdot \sqrt{3}
|
-448 |
(e^{\pi i/4})^{12} = e^{12 \pi i/4}
|
13,121 |
{3 \choose 2} {6 \choose 3} = 60
|
23,422 |
\sin{z} = \sin(1 + z + (-1)) = \sin{1} \cos(z + (-1)) + \sin(z + (-1)) \cos{1}
|
32,521 |
10 = \sqrt{0^2 + D_x^2} \Rightarrow 10 = |D_x|
|
2,861 |
\frac{1}{44} = -\frac{1}{11} + 1/33 + 1/12
|
26,227 |
Y \cdot J = J \cdot Y
|
28,046 |
\frac{(2 + f)^3 + 8 (-1)}{2 + f + 2 (-1)} = (12 f + 6 f^2 + f^3)/f = 12 + 6 f + f^2
|
21,262 |
yN xN/\left(yN\right) = yN xN N/y = yx/y N
|
29,506 |
-n + n^2 \cdot n = n \cdot (n + (-1)) \cdot \left(1 + n\right)
|
18,948 |
1 = (z + y)^2 \leq 2*(z^2 + y * y)
|
-2,827 |
\sqrt{25} \cdot \sqrt{5} + \sqrt{16} \cdot \sqrt{5} = 5 \cdot \sqrt{5} + 4 \cdot \sqrt{5}
|
6,952 |
\frac{3 + 4\cdot \left(-1\right)}{5 + 2\cdot (-1)} = -\dfrac13
|
1,358 |
\left(84 - 2\times M + 15 = M \Rightarrow 99 = M\times 3\right) \Rightarrow 33 = M
|
24,816 |
\frac{1}{n^2 \cdot n \cdot 3} = \frac{1/n}{3 \cdot n \cdot n}
|
1,774 |
33600 = \binom{6}{3} \times \binom{6}{3} \times \binom{9}{3}
|
27,450 |
\left(2 - x = n\times x \implies 2 = (n + 1)\times x\right) \implies x = \tfrac{2}{1 + n}
|
-29,567 |
\left(2 + z^5 + z\cdot 6\right)/z = z^5/z + z\cdot 6/z + \dfrac{2}{z}
|
23,766 |
z^{\frac1e} = z^{\dfrac1e}
|
5,766 |
Z_1 \cap Z_1 \cap Z_2^\complement = Z_1 \cap (Z_1^\complement \cup Z_2^\complement) = (Z_1 \cap Z_1^\complement) \cup (Z_1 \cap Z_2^\complement)
|
22,205 |
\frac{\partial}{\partial t} d_2*d_1 + \frac{\partial}{\partial t} d_1*d_2 = \frac{\partial}{\partial t} (d_2*d_1)
|
23,293 |
(-y)^k = (-y)^k = (-1)^k \cdot y^k
|
-15,682 |
\frac{z^4}{\tfrac{1}{z^4 \frac{1}{r^2}}} = \frac{1}{r^2 \frac{1}{z^4}}z^4
|
-18,425 |
\frac{k\times (5\times (-1) + k)}{(k + 5\times (-1))\times (k + 6\times \left(-1\right))} = \frac{k^2 - 5\times k}{30 + k^2 - k\times 11}
|
16,311 |
\tfrac{1}{k^2} \cdot k \cdot c = c/k
|
-5,487 |
\frac{1}{5(y + 2\left(-1\right))}4 = \dfrac{1}{10 (-1) + 5y}4
|
24,838 |
\mathbb{E}(V) \cdot \mathbb{E}(W) = \mathbb{E}(V \cdot W)
|
-1,333 |
\frac{(-2)\cdot 1/9}{3\cdot 1/2} = 2/3\cdot (-2/9)
|
-20,879 |
\frac{(-30) \cdot z}{z \cdot 18 + 36 \cdot (-1)} = \dfrac{(-1) \cdot 5 \cdot z}{3 \cdot z + 6 \cdot (-1)} \cdot 6/6
|
25,547 |
-5^{\frac13}/2 + 1 = -\dfrac{1}{\left(\frac{8}{5}\right)^{\frac{1}{3}}} + 1
|
19,511 |
\dfrac{\frac{1}{2}}{2}*1 = 1/(2*2) = \frac{1}{4}
|
24,959 |
3/4 = \frac{\frac{\sqrt{3}}{2}\cdot \sqrt{3}}{2}
|
-8,717 |
270^{\frac13} = (3\cdot 3\cdot 3)^{\frac{1}{3}}\cdot (2\cdot 5)^{\dfrac{1}{3}} = 3\cdot (2\cdot 5)^{1/3} = 3\cdot 10^{1/3}
|
16,724 |
x\cdot h\cdot x = \frac{1}{\frac{1}{x - 1/h} - 1/x} + x
|
32,427 |
\frac{0}{1} = \tfrac12 0
|
-16,990 |
-8 = -8\times (-q) - -48 = 8\times q + 48 = 8\times q + 48
|
27,625 |
π/4 = y \implies \cos^5\left(y\right) - \sin^5(y) = 0 \neq \cos(5 \cdot π/4)
|
5,706 |
g^3 + (-1) = (g + (-1))\cdot (g^2 + 2\cdot g + 1 - g) = (g + \left(-1\right))\cdot (g^2 + g + 1)
|
-6,098 |
\dfrac{1}{(z + 9)\cdot 4}\cdot 5 = \frac{5}{4\cdot z + 36}
|
42,288 |
43 = 50 + 7 (-1)
|
8,277 |
x + b'' + c = c + x + b''
|
26,117 |
12\cdot \left(-1\right) + 243 = 231
|
2,122 |
XDZ/Z = DZX/Z
|
20,785 |
z/4 = z^2 + y * y = -y \implies -y*4 = z
|
23,519 |
x = \sec{\theta} \cdot 3 \implies \sec{\theta} = x/3
|
-22,369 |
35 (-1) + m^2 - 2m = (m + 7(-1)) (m + 5)
|
33,127 |
(-1)^{i + 1} = \left(-1\right)^{i + (-1) + 2} = (-1)^{i + \left(-1\right)}\cdot (-1)^2 = \left(-1\right)^{i + \left(-1\right)}
|
10,762 |
\frac{1}{2}\times (-\frac{1}{3 + 2\times x} + 1) = \tfrac{x + 1}{3 + x\times 2}
|
9,926 |
\sin^4{y}*\cos^2{y} = \sin^4{y}*\left(1 - \sin^2{y}\right) = \sin^4{y} - \sin^6{y}
|
5,551 |
\lambda = \lambda + 0*\left(-1\right)
|
-6,099 |
\frac{2}{k^2 + k\cdot 4 + 60\cdot (-1)} = \dfrac{2}{\left(k + 6\cdot (-1)\right)\cdot (10 + k)}
|
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